References

  1. Adams D.R. A note on Riesz potentials. Duke Math. J. 1975, 42, 765–778. doi:10.1215/S0012-7094-75-04265-9
  2. Almeida A., Hasanov J., Samko S. Maximal and potential operators in variable exponent Morrey space. Georgian Math. J. 2008 15 (2), 195–208.
  3. Bennett C., Sharpley R. Interpolation of Operators. In: Pure and Applied Mathematics, 129. Academic Press, USA, 1988.
  4. Burenkov V.I., Guliyev H.V. Necessary and sufficient conditions for boundedness of the maximal operator in local Morrey-type spaces. Studia. Math. 2004, 163, 157–176. doi:10.4064/sm163-2-4
  5. Burenkov V.I., Guliyev H.V., Guliyev V.S. Necessary and sufficient conditions for the boundedness of fractional maximal operator in the local Morrey-type spaces. J. Comput. Appl. Math. 2007, 208 (1), 280–301. doi:10.1016/j.cam.2006.10.085
  6. Burenkov V.I., Guliyev V.S., Tararykova T.V., Serbetci A. Necessary and sufficient conditions for the boundedness of genuine singular integral operators in local Morrey-type spaces. Dokl. Math. 2008, 78, 651–654. doi:10.1134/S1064562408050025
  7. Burenkov V.I., Guliyev V.S. Necessary and sufficient conditions for the boundedness of the Riesz potential in local Morrey-type spaces. Potential Anal. 2009, 30 (3), 211–249. doi:10.1007/s11118-008-9113-5
  8. Burenkov V., Gogatishvili A., Guliyev V.S., Mustafayev R. Boundedness of the fractional maximal operator in local Morrey-type spaces. Complex Var. Elliptic Equ. 2010, 55 (8–10), 739–758. doi:10.1080/17476930903394697
  9. Burenkov V., Nursultanov E.D. Description of interpolation spaces for local Morrey-type spaces. Proc. Steklov Inst. Math. 2010, 269, 46–56. doi:10.1134/S0081543810020045
  10. Cheung K.L., Ho K.-P. Boundedness of Hardy-Littlewood maximal operator on block spaces with variable exponent. Czechoslovak Math. J. 2014, 64 (1), 159–171. doi:10.1007/s10587-014-0091-z
  11. Diening L. Maximal function on Musielak-Orlicz spaces and generalized Lebesgue spaces. Bull. Sci. Math. 2005, 129, 657–700. doi:10.1016/j.bulsci.2003.10.003
  12. Diening L., Harjulehto P., Hästö P., Ružička M. Lebesgue and Sobolev Spaces with Variable Exponents. In: Morel J.-M., Teissier B. (Eds.) Lecture notes in mathematics, 2017. Springer, Heidelberg, 2011.
  13. García-Cuerva J. Weighted \(H^{p}\) spaces. Instytut Matematyczny Polskiej Akademi Nauk, Warszawa, 1979.
  14. Grafakos L. Modern Fourier Analysis. In: Axler S., Ribet K. (Eds.) Graduate Texts in Mathematics, 250. Springer-Verlag, New York, 2009.
  15. Guliyev V.S. Generalized local Morrey spaces and fractional integral operators with rough kernel. J. Math. Sci. 2013, 193, 211–227. doi:10.1007/s10958-013-1448-9
  16. Ho K.-P. Atomic decompositions of Hardy spaces and characterization of \(BMO\) via Banach function spaces. Anal. Math. 2012, 38 (3), 173–185. doi:10.1007/s10476-012-0302-5
  17. Ho K.-P. Fractional integral operators with homogeneous kernels on Morrey spaces with variable exponents. J. Math. Soc. Japan 2017, 69 (3), 1059–1077. doi:10.2969/jmsj/06931059
  18. Ho K.-P. Singular integral operators and sublinear operators on Hardy local Morrey spaces with variable exponents. Bull. Sci. Math. 2021, 171, 103033. doi:10.1016/j.bulsci.2021.103033
  19. Ho K.-P. Boundedness of operators and inequalities on Morrey-Banach spaces. Publ. Res. Inst. Math. Sci. 2022, 58 (3), 551–577. doi:10.4171/PRIMS/58-3-4
  20. Ho K.-P. Calderón-Zygmund operators, Bochner-Riesz means and parametric Marcinkiewicz integrals on Hardy-Morrey spaces with variable exponents. Kyoto J. Math. 2023, 63 (2), 335–351. doi:10.1215/21562261-10428475
  21. Ho K.-P. Fractional geometrical maximal functions on Morrey spaces with variable exponents. Results Math. 2022, 77, article number 32. doi:10.1007/s00025-021-01570-8
  22. Krantz S. Fractional integration on Hardy spaces. Studia Math. 1982, 73 (2), 87–94.
  23. Kokilashvili V., Meskhi A. Boundedness of maximal and singular operators in Morrey spaces with variable exponent. Armen. J. Math. 2008, 1 (1), 18–28.
  24. Macias R., Segovia C. Weighted norm inequalities for parabolic fractional integrals. Studia Math. 1977, 61, 279–291. doi:10.4064/SM-61-3-279-291
  25. Morrey C. On the solutions of quasi-linear elliptic partial differential equations. Trans. Amer. Math. Soc. 1938, 43, 126–166. doi:10.1090/S0002-9947-1938-1501936-8
  26. Muckenhoupt B., Wheeden R. Weighted norm inequalities for singular and fractional integrals. Trans. Amer. Maths. Soc. 1971, 161, 249–258. doi:10.1090/S0002-9947-1971-0285938-7
  27. Muckenhoupt B., Wheeden R. Weighted norm inequalities for fractional integrals. Trans. Amer. Math. Soc. 1974, 192, 261–274. doi:10.1090/S0002-9947-1974-0340523-6
  28. Peetre J. On the theory of \({\cal L}_{p,\lambda}\) spaces. J. Funct. Anal. 1969, 4 (1), 71–87. doi:10.1016/0022-1236(69)90022-6
  29. Ragusa M.A. Commutators of fractional integral operators on vanishing-Morrey spaces. J. Global Optim. 2008, 40, 361–368. doi:10.1007/s10898-007-9176-7
  30. Ragusa M.A. Embeddings for Morrey-Lorentz spaces. J. Optim. Theory Appl. 2012, 154 (2), 491–499. doi:10.1007/s10957-012-0012-y
  31. Rubio de Francia J.L. Factorization and extrapolation of weights. Bull. Amer. Math. Soc. (N.S.) 1982, 7 (2),393–395.
  32. Rubio de Francia J.L. A new technique in the theory of \(A_{p}\) weights. In Topics in modern harmonic analysis, Vol. I, II. Turin/Milan, 1982, 571–579. Ist. Naz. Alta Mat. Francesco Severi, Rome, 1983.
  33. Rubio de Francia J.L. Factorization theory and \(A_{p}\) weights. Amer. J. Math. 1984, 106 (3), 533–547. doi:10.2307/2374284
  34. Sawano Y., Sugano T., Tanaka H. Orlicz-Morrey spaces and fractional operators. Potential Anal. 2012, 36, 517–556. doi:10.1007/s11118-011-9239-8
  35. Sawano Y., Ho K.-P., Yang D., Yang S. Hardy spaces for ball quasi-Banach function spaces. Dissertationes Math. 2017, 525, 1–102. doi:10.4064/dm750-9-2016
  36. Stein E., Weiss G. On the theory of harmonic functions of several variables: I. The theory of \(H^{p}\)-spaces. Acta Math. 1960, 103 (1–2), 25–62. doi:10.1007/BF02546524
  37. Stein E.M. Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals. In: Princeton Mathematical Series, 43. Princeton Univ. Press, Princeton, NJ, 1993.
  38. Strömberg J.-O., Torchinsky A. Weighted Hardy Spaces. In: Dold A., Eckmann B. (Eds.) Lecture Notes in Mathematics, 1381. Springer, New York, 1989.
  39. Yee T.-L., Ho K.-P., Cheung K.L., Suen C.K. Local sharp maximal functions, geometrical maximal functions and rough maximal functions on local Morrey spaces with variable exponents. Math. Inequal. Appl. 2020, 23 (4), 1509–1528. doi:10.7153/mia-2020-23-108
  40. Yee T.-L., Ho K.-P. Fractional integral operators with homogeneous kernels on generalized Lorentz-Morrey spaces. J. Math. Inequal. 2021, 15 (1), 17–30. doi:10.7153/jmi-2021-15-03